All materials radiate (emit) energy at a rate and at wavelengths determined by the temperature of the material, and by a property of the material referred to as its emissivity. Emissivity is defined as the ratio of the power radiated by a material at a given temperature to the power radiated by a blackbody (a "perfect" emitter) at the same temperature. Emissivity depends on the temperature of the material, the angle from which the surface of the material is viewed, and on wavelength.
The general concept of emissivity is illustrated in FIGS. 1A and 1B. In FIG. 1A, curve 12 represents the spectral radiance (for example in watts/cm.sup.3 /steradian) of a material at a particular temperature, as a function of wavelength. Curve 14 represents the spectral radiance of a perfect blackbody at the same temperature. The emissivity of this material, represented by curve 16 in FIG. 1B, is the ratio of the radiance of the material (curve 12) to the radiance of the blackbody (curve 14). Since a blackbody is by definition a perfect radiator, the emissivities of passive materials are always less than one.
It is desirable for many reasons to be able to accurately and routinely measure the emissivities of a broad range of different materials. As examples, emissivity measurements are used for basic materials research, for calculating the infrared detectability of military targets, and for calculating thermal balances in aircraft, spacecraft and other structures and systems. At present, however, accurate emissivity measurements can be made only on a limited range of materials, for reasons explained below. Furthermore, within that range, extraordinary care must be taken with materials that do not have high values of thermal conductivity.
The fundamental problem in making an accurate emissivity measurement is that it is difficult to obtain a sufficiently accurate measurement of the temperature of the material at the region where radiation is emitted. The temperature must be known accurately because there is a large change in the power radiated by a material when its temperature changes by even a small amount. (For a blackbody, the total radiated power summed over all wavelengths depends on the fourth power of the absolute temperature.) This temperature sensitivity is illustrated by curve 18 in FIG. 1A. Curve 18 represents the spectral radiance that might be measured for a blackbody source having a temperature slightly lower than the target temperature for the emissivity measuremeier. The shift between curves 14 and 18 would introduce a large error in determination of emissivity. By way of example, to obtain one percent accuracy in an emissivity measurement at a wavelength of 6 microns of a material at 220 Kelvins (about -65.degree. F.), temperature must be known to an accuracy of 0.2 Kelvins. The temperature accuracy required to obtain one percent accuracy in an emissivity measurement is shown as a function of wavelength in FIG. 1C for three different material temperatures.
In the past, the physical conditions under which emissivity measurements must be obtained have made accurate temperature measurement extremely difficult for some materials, and nearly impossible for most. To measure emissivity, the sample of material must generally be placed in an environment which is very cold relative to the material. This step is to ensure that thermal radiation from the surrounding environment is low enough so that the radiation originating from the environment and reflected or scattered by the material is negligible compared to radiation originating from the material itself. However, if the material sample is much warmer than the environment, then the sample will have a tendency to cool rapidly. To compensate for this tendency, there must be a constant flow of heat from within the material to the material's surface. However, heat flow within a material requires a temperature gradient as a driver. A material having a relatively low thermal conductivity might require a temperature gradient of several hundred degrees Celsius per inch to maintain a relatively moderate surface temperature in a cold environment.
This temperature gradient problem is illustrated in FIG. 2. Assume that it is desired to measure the emissivity of a material having a low thermal conductivity, such as polyethylene. A material 20 is formed in a layer 0.1 inches thick on a metal substrate 22. A line 26 shows the temperature profile within material 20 that would be required to maintain a surface 24 of the material at a temperature of 480 Kelvins. As illustrated, a temperature gradient of about 18.6 Kelvins across a sample of thickness 0.1 inches would be required to compensate for radiative heat loss (assuming a surface emissivity of 0.8 with no return radiation from the surrounding environment). Under these conditions, it is not possible to obtain an accurate temperature measurement from a thermometer placed within the material, because the temperature within the material varies significantly from the surface temperature. It might appear that the solution to this problem would be to place the thermometer outside of material 20, touching its surface 24. However, such a thermometer will radiate energy at a rate characteristic of the thermometer material, rather than of the sample, and alter the heat flow balance necessary to maintain surface temperature. The act of measuring surface temperature would change the quantity being measured.
With existing technology, it is possible to measure the emissivity of some materials that have high thermal conductivities. For such materials, the temperature gradient required to maintain heat flow is sufficiently small so that adequate temperature accuracy can be obtained from a thermometer placed within the material.
It is also possible, with great difficulty, to measure the emissivity of a material having a low thermal conductivity if that material is opaque to thermal radiation at all wavelengths of interest. Thermal radiation emitted by an opaque material can be assumed to originate at the material surface. But the temperature of the material surface can be obtained accurately enough only through extremely precise measurements of heat flow through the material, thermal conductivity of the material, material thickness, and the temperature of the material back side (the equivalent with respect to FIG. 2 of the point where temperature is 498.6 Kelvins).
However, most materials having moderate or low thermal conductivities are not completely opaque to thermal radiation; and the degree of opacity or, conversely, of transparency, can vary considerably from one wavelength to another. Thermal radiation from such a material can originate within the body of the material, at varying distances from the material surface. Since these materials would contain a large temperature gradient under the necessary measurement environment, a unique temperature cannot be associated with the thermal radiation; and, a unique temperature is a necessary element of an emissivity measurement.
A solution to these problems is to place the material in an isothermal condition, that is, to make the material temperature constant everywhere within the material. In this case, a thermometer can be placed anywhere within the material (except near the surface of a material sufficiently non-opaque so that thermal radiation from the thermometer can reach the surface).
It might be thought possible to measure emissivity by placing a sample material in a thermal chamber until it has reached thermal equilibrium, i.e., an isothermal condition. The thermal chamber would then be opened for a period of time long enough to permit a measurement of the spectrum of radiation from the sample. Unfortunately, since the environment surrounding the thermal chamber must be very cold compared to the chamber, opening of the thermal chamber will cause the surface of the material to begin cooling too fast to permit accurate emissivity measurements. For example, it can be shown through thermal modeling that if a material sample has the same thermal properties (specifically, thermal diffusivity) as Teflon but an emissivity of 0.9, and if the sample is at a temperature of 480 Kelvins, then, through thermal radiation alone, the surface temperature of the sample will drop by about 0.41 Kelvins within 0.01 seconds after exposure of the sample to the cold external environment. This interval is far too brief to permit an accurate spectrum of the material to be measured.